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-this is a Least Common Multiple Problem guys……Right off the top, based on question alone, K could not be “0” because the question asks if integer K have at least 3 different positive prime numbers (btw, there is no such things as a non-positive prime number by definition of what a prime number is……recall the first prime number is 2….), in which “0” doesn’t have factors…………

What number evenly divides into zero? What number is a factor of zero?

Check it out:

(i) K/15 is an integer….means that K has to be a most 15 in order for it to be an integer, however, K could be 30, 45, 60, etc

-statement one also states that K/15 is an integer which implies that 15 is a factor of K. the least factor in which K/15 is an integer is 15 and if you were to perform prime factorization on 15 you get 15=3x5…..only two prime factors. INSUFFICIENT BECAUSE WE DON’T KNOW IF K = 15, 30, ETC…..

(ii) assess statement (ii) similar to one and you will see the same result. The only prime factors in which K has to be at least 10 in order to be an integer is 10. and the prime factorization of 10 = 5x2….only two prime factors.

Taking (i) and (ii) together in which K/15 = an integer and K/10 is an integer, the least common multiple of K=2*3*5=30, which means that K has at least 3 positive prime factors (2,3,5)

Combining statements 1 and 2 we know that 2, 3 and 5 are all prime factors of k.

Thus integer k has "at least three different positive prime factors".

Yes.

Answer is C.

Footnote: if k were 0 then the answer would still be Yes, as all numbers are factors of 0, and all primes are factors of 0. Therefore integer k would still have "at least three different positive prime factors". _________________

If this were a real GMAT question, it would ask "Does the positive integer K have at least three different positive prime factors?" GMAT questions about divisibility are always restricted to positive integers only. That said, zero is not an exception here anyway, as has been pointed out above, but you won't need to worry about that on the real test. _________________

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If this were a real GMAT question, it would ask "Does the positive integer K have at least three different positive prime factors?" GMAT questions about divisibility are always restricted to positive integers only. That said, zero is not an exception here anyway, as has been pointed out above, but you won't need to worry about that on the real test.

Agree with you. In a topic, someone said that, GMAC's cost per question is about 2 thousand dollars; so, these questions are very well designed.